Peer-reviewedCC BYGroups, Geometry, and Dynamics
Groups with property (T) and many alternating group quotients
Abstract
We prove that, for the free algebra over a sufficiently rich operad \mathcal{O} , a large subgroup of its group of tame automorphisms has Kazhdan’s property (T). We deduce that there exists a group with property (T) that maps onto large powers of alternating groups.
Related
- Essential quotients of the cohomology of products of symmetric and alternating groups
- Property (T) and nonlinearity of mapping class group quotients
- Computable presentations of reduced group C*-algebras of groups with the rapid decay property
- Infinitely many Nielsen classes in mapping class groups and free-group automorphism groups
- Kazhdan's Property (T) for Subspaces and Quotients of Lp-Spaces
BibTeX
@article{bartholdi2026groups,
title = {{Groups with property (T) and many alternating group quotients}},
author = {Laurent Bartholdi and Martin Kassabov},
journal = {Groups, Geometry, and Dynamics},
year = {2026},
month = nov,
doi = {10.4171/ggd/892},
url = {https://hal.science/hal-05849735v1},
note = {CC BY},
}
RIS
TY - JOUR
TI - Groups with property (T) and many alternating group quotients
AU - Laurent Bartholdi
AU - Martin Kassabov
PY - 2026
DA - 2026/11/03
JO - Groups, Geometry, and Dynamics
DO - 10.4171/ggd/892
UR - https://hal.science/hal-05849735v1
AB - We prove that, for the free algebra over a sufficiently rich operad \mathcal{O} , a large subgroup of its group of tame automorphisms has Kazhdan’s property (T). We deduce that there exists a group with property (T) that maps onto large powers of alternating groups.
SN - 1661-7207
SN - 1661-7215
ER -